sl(<i>N</i>)–link homology (<i>N</i>≥ 4) using foams and the Kapustin–Li formula

Vaz, Pedro; Mackaay, Marco; Stošić, Marko

doi:10.2140/gt.2009.13.1075

Cited by 60 publications

(91 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The case of higher rank gauge groups has been also studied in the context of bi-graded homology theory, which brought about the colored sl N homology H sl N ,R i,j [15][16][17][18]. The Poincaré polynomial of the colored sl N homology…”

Section: Su (N )mentioning

confidence: 99%

Super-A-polynomials for twist knots

Nawata

Ramadevi

Zodinmawia

et al. 2012

J. High Energ. Phys.

View full text Add to dashboard Cite

We conjecture formulae of the colored superpolynomials for a class of twist knots K p where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomials for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed Apolynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.

show abstract

Section: Su (N )mentioning

confidence: 99%

Super-A-polynomials for twist knots

Nawata

Ramadevi

Zodinmawia

et al. 2012

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…1, where the identity map x → x in the LHS corresponds to the annular cobordism in the left of the figure, and the sum involving the Frobenius form ǫ is depicted in the right of the figure. [13] as follows. The multiplication and the unit are defined by those for polynomials, the Frobenius form (counit) ǫ is defined by ǫ(1) = ǫ(X) = 0, ǫ(X 2 ) = −1.…”

Section: Preliminarymentioning

confidence: 99%

“…For TQFTs we refer to [11]. We follow definitions of foams in [9,13], except that facets of foams are decorated by basis elements of A, in a general way as in [6]. A foam without boundary is called closed.…”

Section: Preliminarymentioning

confidence: 99%

“…For categorifications of other knot invariants, 2-dimensional complexes called foams have been used instead [9,13]. Although 2D-TQFT has been characterized [11] in terms of commutative Frobenius algebras, foams have not been algebraically characterized in terms of TQFT.…”

Section: Introductionmentioning

confidence: 99%

“…Although 2D-TQFT has been characterized [11] in terms of commutative Frobenius algebras, foams have not been algebraically characterized in terms of TQFT. Relations to Lie algebras, for example, have been suggested [9,13] through their boundaries which are called webs and that are trivalent graphs. Foams have branch curves along which three sheets meet.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Algebraic Structures Derived from Foams

Carter¹,

Saito²

2011

J. Gen. Lie Theory Appl.

View full text Add to dashboard Cite

Foams are surfaces with branch lines at which three sheets merge. They have been used in the categorification of sl(3) quantum knot invariants and also in physics. The 2D-TQFT of surfaces, on the other hand, is classified by means of commutative Frobenius algebras, where saddle points correspond to multiplication and comultiplication. In this paper, we explore algebraic operations that branch lines derive under TQFT. In particular, we investigate Lie bracket and bialgebra structures. Relations to the original Frobenius algebra structures are discussed both algebraically and diagrammatically.

show abstract